The discussion of injectivity of the sampling operator for a union of MI spaces in the collection \(\lbrace \mathcal {N}_\delta \rbrace _{\delta \in \Delta }\)  comes with a problem. The definition of an injective operator (say \(A\) ) says that for any \(x_1,x_2 \)  in the domain of the operator, \(Ax_1 = Ax_2\)  implies \(x_1=x_2.\)  The issue while considering the union of subspaces is that the points \(x_1\)  and \(x_2\)  can be from different subspaces of the union and exploits the linearity. To deal with the issue, we consider the union of a sum of MI subspaces of \(L^2(X;\mathcal {H}).\)  The idea was originated in [1]} and supported further by [2]} where they considered the collection \(\lbrace \mathcal {S}_\delta \rbrace _{\delta \in \Delta }\)  of shift invariant spaces and took the union of a sum of each shift invariant space in the collection. Similarly, we consider the union
\(\mathcal {X}: =\bigcup _{\delta \in \Delta }\mathcal {N}_{\delta ,\theta }\) 
